Question

How do I solve Sigma(a^n + nb) where n=1 to n=10? Preferably without a calculator or Wolfram

Answer 1

\[\sum_{n=1}^{10}a ^{n}+nb\]

Answer 2

\[\sum\limits_{n=1}^{10}(a^n+nb)=(a+a^2+\cdots+a^{10})+(b+2b+\cdots+10b)=\]
\[=a\frac{1-a^{10}}{1-a}+55b\]